
'''simple docstring'''

from __future__ import annotations

from collections.abc import Generator







def     snake_case__						(   )			->   Dict:
		_UpperCamelCase							:			dict[int, int]     =   {}
		_UpperCamelCase							:			Optional[Any]     =   2
		while True:
				_UpperCamelCase							:			Optional[Any]     =   factor_map.pop(_A      ,_A						)
				if factor:
						_UpperCamelCase							:			Dict     =   factor + prime
						while x in factor_map:
								x += factor
						_UpperCamelCase							:			Optional[Any]     =   factor
				else:
						_UpperCamelCase							:			Tuple     =   prime
						yield prime
				prime += 1







def     snake_case__						(   UpperCamelCase = 1e10						)			->   Optional[Any]:
		_UpperCamelCase							:			Union[str, Any]     =   sieve()

		_UpperCamelCase							:			Any     =   1
		while True:
				_UpperCamelCase							:			List[Any]     =   next(_A						)
				if (2 * prime * n) > limit:
						return n
				# Ignore the next prime as the reminder will be 2.
				next(_A						)
				n += 2


if __name__ == "__main__":
	print(solution())










'''simple docstring'''






from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_torch_available,
)


lowerCAmelCase:   Dict					=		{'configuration_vit_mae': ['VIT_MAE_PRETRAINED_CONFIG_ARCHIVE_MAP', 'ViTMAEConfig']}

try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     lowerCAmelCase:   Optional[int]					=		[
         'VIT_MAE_PRETRAINED_MODEL_ARCHIVE_LIST',
         'ViTMAEForPreTraining',
         'ViTMAELayer',
         'ViTMAEModel',
         'ViTMAEPreTrainedModel',
     ]

try:
     if not is_tf_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     lowerCAmelCase:   List[Any]					=		[
         'TFViTMAEForPreTraining',
         'TFViTMAEModel',
         'TFViTMAEPreTrainedModel',
     ]

if TYPE_CHECKING:
     from .configuration_vit_mae import VIT_MAE_PRETRAINED_CONFIG_ARCHIVE_MAP, ViTMAEConfig

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_vit_mae import (
              VIT_MAE_PRETRAINED_MODEL_ARCHIVE_LIST,
              ViTMAEForPreTraining,
              ViTMAELayer,
              ViTMAEModel,
              ViTMAEPreTrainedModel,
          )

     try:
          if not is_tf_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_tf_vit_mae import TFViTMAEForPreTraining, TFViTMAEModel, TFViTMAEPreTrainedModel


else:
     import sys

     lowerCAmelCase:   Tuple					=		_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)